Bayes-Nash Equilibrium of the Generalized First-Price Auction

We analyze the generalized first-price auction under incomplete information setting. Without setting a reserve price, the efficient symmetrical Bayes-Nash equilibrium is characterized and found to be increasing as the number of bidders is sufficiently large. Then, the explicit expression for the expected revenue of the search engine is found and the effect of the click rates of all the positions on the expected revenue is obtained. Finally, with setting of the reserve price, we have found the optimal reserve price and examine how the difference of the search engine’s revenues with setting reserve price and without setting reserve price varies with the reserve price.